The U.S. military command in Baghdad said that besides the 10 U.S. troops killed in Fallujah, two members of the Iraqi security forces also had been killed. A brief U.S. military statement said there could be delays in reporting combat casualties in Fallujah "in order to prevent the anti-Iraqi forces and other terrorist elements from gaining useful battlefield intelligence."

Lt. Gen. Thomas Metz, the senior American commander for the Fallujah operation, said he was pleased that U.S. casualties so far were relatively light, considering the dangers of urban combat.

Speaking by video teleconference from his headquarters in Baghdad, Metz told reporters at the Pentagon that insurgent casualties were "significantly higher than I expected." Most of the rebel force, estimated at between 2,000 and 3,000, was "fighting hard but not to the death," he said.

Casualty reports, particularly in a combat zone like Fallujah, sometimes are slow and imprecise because of the chaotic conditions.

Tommy Franks, the retired four-star Army general who commanded U.S. forces when President Bush ordered the invasion in March 2003, said Tuesday it was too early to conclude that American casualties would remain light.

"There can be an inclination to say, "Hey, this is going just right.' I'd caution against that," he said in an Associated Press interview. "This enemy is capable of putting up a big fight."

Franks also said he expected the level of violence in Iraq, as well as the number of American casualties, to begin to decline now that the U.S. elections were over and Bush had made clear that the United States would remain on course.

On Monday, 11 U.S. service members died across Iraq - among the highest for a single day since last spring - as the insurgents escalated the violence in Baghdad and elsewhere.

The death toll for Iraqi civilians has been higher in recent days than the U.S. death count, as it has been through much of the war. Many have been killed by car bombs.

Dan Goure, a military analyst at the Lexington Institute think tank, said Iraqis present an easier target for the insurgents, and he expects them to continue to bear the brunt of the violence.

Goure said the relatively light American casualties in the opening days of the Fallujah offensive may not hold as the fighting escalates. But he noted that so far the toll is less severe than last April when 135 U.S. troops died, the worst month of the war.

"If casualties in November start approaching that number, then there's some significant reason to worry," Goure said.

After a decline in U.S. deaths in May and June, the toll began rising again. There were 54 in July, 65 in August, 80 in September and 63 in October. By the Pentagon's count, 1,139 Americans have died in Iraq since the U.S.-led invasion in March 2003.

Metz said it was remained unclear whether insurgents were consolidating in parts of the city that U.S. forces had not yet reached. In any case he foresaw "several more days of tough urban fighting."

U.S. officials have been predicting for weeks that violence in Iraq would escalate as national elections scheduled for January drew closer. They believe the rebels' main goal is to prevent the elections.

The U.S.-led assault on Fallujah, while risking a spike in casualties, is intended to stabilize that city so that a major population center is not excluded from the January voting.

The insurgents remain a problem in several other cities in the "Sunni Triangle" that runs north and west from Baghdad, where deposed President Saddam Hussein grew up and had his strongest support. These include Ramadi, Baqubah, Samarra and the Iraqi capital.

The Fallujah fighting is among the most dangerous for U.S. troops, who are battling bands of guerrillas in the city's streets. Among the threats they face are hidden roadside bombs and car bombs, in addition to small arms like AK-47 assault rifles and machine guns.

There also is an increased risk of "friendly fire" casualties in urban warfare, although there was no indication Tuesday that this had happened.

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